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We analyze optimal pollution standards and enforcement strategies in settings where environmental damages depend on accumulated pollution, and enforcement is socially costly. We assume that a regulator and a representative polluting firm interact in a Stackelberg differential game, and we specifically allow the firm to pollute above the limit, and pay the corresponding fine. A crucial element is how progressive the fine is with respect to the degree of non-compliance. Some of our results contradict the related literature on the control of stock pollutants under full-compliance. In particular, we find that setting standards dependent on the pollution stock (setting quantities) is preferred if fines are sufficiently non-linear; while setting fines dependent on the pollution stock (setting prices) is preferred if fines are linear or almost linear, and specially when the environmental problem is particularly harmful.